14.115 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.019 * * * [progress]: [2/2] Setting up program. 0.020 * [progress]: [Phase 2 of 3] Improving. 0.021 * [simplify]: Simplifying using # : (/ a (neg (acos a))) 0.023 * * [simplify]: iteration 0 : 4 enodes (cost 3 ) 0.023 * [simplify]: Simplified to: (/ a (neg (acos a))) 0.023 * * [progress]: iteration 1 / 4 0.023 * * * [progress]: picking best candidate 0.024 * * * * [pick]: Picked # 0.024 * * * [progress]: localizing error 0.028 * * * [progress]: generating rewritten candidates 0.028 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.034 * * * [progress]: generating series expansions 0.035 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.035 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.035 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.035 * [taylor]: Taking taylor expansion of -1 in a 0.035 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.035 * [taylor]: Taking taylor expansion of a in a 0.035 * [taylor]: Taking taylor expansion of (acos a) in a 0.035 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.035 * [taylor]: Taking taylor expansion of -1 in a 0.035 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.035 * [taylor]: Taking taylor expansion of a in a 0.035 * [taylor]: Taking taylor expansion of (acos a) in a 0.042 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.042 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.042 * [taylor]: Taking taylor expansion of -1 in a 0.042 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.042 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.042 * [taylor]: Taking taylor expansion of a in a 0.042 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.042 * [taylor]: Taking taylor expansion of -1 in a 0.042 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.042 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.043 * [taylor]: Taking taylor expansion of a in a 0.048 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.048 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.048 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.048 * [taylor]: Taking taylor expansion of a in a 0.048 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.049 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.049 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.049 * [taylor]: Taking taylor expansion of a in a 0.049 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.057 * * * [progress]: simplifying candidates 0.058 * [simplify]: Simplifying using # : (- (log a) (log (neg (acos a)))) (log (/ a (neg (acos a)))) (exp (/ a (neg (acos a)))) (/ (* (* a a) a) (* (* (neg (acos a)) (neg (acos a))) (neg (acos a)))) (* (cbrt (/ a (neg (acos a)))) (cbrt (/ a (neg (acos a))))) (cbrt (/ a (neg (acos a)))) (* (* (/ a (neg (acos a))) (/ a (neg (acos a)))) (/ a (neg (acos a)))) (sqrt (/ a (neg (acos a)))) (sqrt (/ a (neg (acos a)))) (neg a) (neg (neg (acos a))) (/ (* (cbrt a) (cbrt a)) (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ (cbrt a) (cbrt (neg (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (neg (acos a)))) (/ (cbrt a) (sqrt (neg (acos a)))) (/ (* (cbrt a) (cbrt a)) 1) (/ (cbrt a) (neg (acos a))) (/ (* (cbrt a) (cbrt a)) -1) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ (cbrt a) (cbrt (acos a))) (/ (* (cbrt a) (cbrt a)) (neg (sqrt (acos a)))) (/ (cbrt a) (sqrt (acos a))) (/ (* (cbrt a) (cbrt a)) (neg 1)) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt a) (neg (cbrt (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) (/ (cbrt a) (neg (sqrt (acos a)))) (/ (* (cbrt a) (cbrt a)) 1) (/ (cbrt a) (neg (acos a))) (/ (sqrt a) (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ (sqrt a) (cbrt (neg (acos a)))) (/ (sqrt a) (sqrt (neg (acos a)))) (/ (sqrt a) (sqrt (neg (acos a)))) (/ (sqrt a) 1) (/ (sqrt a) (neg (acos a))) (/ (sqrt a) -1) (/ (sqrt a) (acos a)) (/ (sqrt a) (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt a) (cbrt (acos a))) (/ (sqrt a) (neg (sqrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (neg 1)) (/ (sqrt a) (acos a)) (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt a) (neg (cbrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (neg (sqrt (acos a)))) (/ (sqrt a) 1) (/ (sqrt a) (neg (acos a))) (/ 1 (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ a (cbrt (neg (acos a)))) (/ 1 (sqrt (neg (acos a)))) (/ a (sqrt (neg (acos a)))) (/ 1 1) (/ a (neg (acos a))) (/ 1 -1) (/ a (acos a)) (/ 1 (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (cbrt (acos a))) (/ 1 (neg (sqrt (acos a)))) (/ a (sqrt (acos a))) (/ 1 (neg 1)) (/ a (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (neg (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ a (neg (sqrt (acos a)))) (/ 1 1) (/ a (neg (acos a))) (/ 1 (neg (acos a))) (/ (neg (acos a)) a) (/ a (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ a (sqrt (neg (acos a)))) (/ a 1) (/ a -1) (/ a (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (neg (sqrt (acos a)))) (/ a (neg 1)) (/ a (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (sqrt (acos a))) (/ a 1) (/ (neg (acos a)) (cbrt a)) (/ (neg (acos a)) (sqrt a)) (/ (neg (acos a)) a) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 0.065 * * [simplify]: iteration 0 : 164 enodes (cost 371 ) 0.068 * * [simplify]: iteration 1 : 483 enodes (cost 359 ) 0.075 * * [simplify]: iteration 2 : 1375 enodes (cost 359 ) 0.095 * * [simplify]: iteration 3 : 3633 enodes (cost 358 ) 0.148 * * [simplify]: iteration 4 : 5001 enodes (cost 358 ) 0.150 * [simplify]: Simplified to: (log (/ a (neg (acos a)))) (log (/ a (neg (acos a)))) (exp (/ a (neg (acos a)))) (pow (/ a (neg (acos a))) 3) (* (cbrt (/ a (neg (acos a)))) (cbrt (/ a (neg (acos a))))) (cbrt (/ a (neg (acos a)))) (pow (/ a (neg (acos a))) 3) (sqrt (/ a (neg (acos a)))) (sqrt (/ a (neg (acos a)))) (* -1 a) (acos a) (/ (* (cbrt a) (cbrt a)) (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ (cbrt a) (cbrt (neg (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (neg (acos a)))) (/ (cbrt a) (sqrt (neg (acos a)))) (* (cbrt a) (cbrt a)) (/ (cbrt a) (neg (acos a))) (/ (* (cbrt a) (cbrt a)) -1) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ (cbrt a) (cbrt (acos a))) (/ (* (cbrt a) (cbrt a)) (neg (sqrt (acos a)))) (/ (cbrt a) (sqrt (acos a))) (/ (* (cbrt a) (cbrt a)) -1) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt a) (neg (cbrt (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) (/ (cbrt a) (neg (sqrt (acos a)))) (* (cbrt a) (cbrt a)) (/ (cbrt a) (neg (acos a))) (/ (sqrt a) (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ (sqrt a) (cbrt (neg (acos a)))) (/ (sqrt a) (sqrt (neg (acos a)))) (/ (sqrt a) (sqrt (neg (acos a)))) (sqrt a) (/ (sqrt a) (neg (acos a))) (/ (sqrt a) -1) (/ (sqrt a) (acos a)) (/ (sqrt a) (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt a) (cbrt (acos a))) (/ (sqrt a) (neg (sqrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) -1) (/ (sqrt a) (acos a)) (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt a) (neg (cbrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (neg (sqrt (acos a)))) (sqrt a) (/ (sqrt a) (neg (acos a))) (/ 1 (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ a (cbrt (neg (acos a)))) (/ 1 (sqrt (neg (acos a)))) (/ a (sqrt (neg (acos a)))) 1 (* -1 (/ a (acos a))) -1 (/ a (acos a)) (/ 1 (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (cbrt (acos a))) (/ 1 (neg (sqrt (acos a)))) (/ a (sqrt (acos a))) -1 (/ a (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (neg (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ a (neg (sqrt (acos a)))) 1 (* -1 (/ a (acos a))) (/ -1 (acos a)) (/ (neg (acos a)) a) (/ a (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ a (sqrt (neg (acos a)))) a (* -1 a) (/ a (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (neg (sqrt (acos a)))) (* -1 a) (/ a (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (sqrt (acos a))) a (/ (neg (acos a)) (cbrt a)) (/ (neg (acos a)) (sqrt a)) (/ (neg (acos a)) a) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 0.151 * * * [progress]: adding candidates to table 0.230 * * [progress]: iteration 2 / 4 0.230 * * * [progress]: picking best candidate 0.244 * * * * [pick]: Picked # 0.244 * * * [progress]: localizing error 0.250 * * * [progress]: generating rewritten candidates 0.250 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.259 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.275 * * * [progress]: generating series expansions 0.275 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.275 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.275 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.275 * [taylor]: Taking taylor expansion of -1 in a 0.275 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.275 * [taylor]: Taking taylor expansion of a in a 0.275 * [taylor]: Taking taylor expansion of (acos a) in a 0.275 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.275 * [taylor]: Taking taylor expansion of -1 in a 0.275 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.275 * [taylor]: Taking taylor expansion of a in a 0.275 * [taylor]: Taking taylor expansion of (acos a) in a 0.287 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.287 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.287 * [taylor]: Taking taylor expansion of -1 in a 0.287 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.287 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.287 * [taylor]: Taking taylor expansion of a in a 0.287 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.287 * [taylor]: Taking taylor expansion of -1 in a 0.287 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.287 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.287 * [taylor]: Taking taylor expansion of a in a 0.293 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.293 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.293 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.293 * [taylor]: Taking taylor expansion of a in a 0.293 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.293 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.293 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.293 * [taylor]: Taking taylor expansion of a in a 0.293 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.302 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.302 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.302 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.302 * [taylor]: Taking taylor expansion of -1 in a 0.302 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.302 * [taylor]: Taking taylor expansion of (acos a) in a 0.302 * [taylor]: Taking taylor expansion of a in a 0.303 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.303 * [taylor]: Taking taylor expansion of -1 in a 0.303 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.303 * [taylor]: Taking taylor expansion of (acos a) in a 0.303 * [taylor]: Taking taylor expansion of a in a 0.316 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.316 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.316 * [taylor]: Taking taylor expansion of -1 in a 0.316 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.316 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.316 * [taylor]: Taking taylor expansion of a in a 0.316 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.316 * [taylor]: Taking taylor expansion of -1 in a 0.316 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.316 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.316 * [taylor]: Taking taylor expansion of a in a 0.327 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.327 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.327 * [taylor]: Taking taylor expansion of a in a 0.327 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.327 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.327 * [taylor]: Taking taylor expansion of a in a 0.328 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.335 * * * [progress]: simplifying candidates 0.338 * [simplify]: Simplifying using # : (neg 1) (neg (- (log (neg (acos a))) (log a))) (neg (log (/ (neg (acos a)) a))) (- 0 (- (log (neg (acos a))) (log a))) (- 0 (log (/ (neg (acos a)) a))) (- (log 1) (- (log (neg (acos a))) (log a))) (- (log 1) (log (/ (neg (acos a)) a))) (log (/ 1 (/ (neg (acos a)) a))) (exp (/ 1 (/ (neg (acos a)) a))) (/ (* (* 1 1) 1) (/ (* (* (neg (acos a)) (neg (acos a))) (neg (acos a))) (* (* a a) a))) (/ (* (* 1 1) 1) (* (* (/ (neg (acos a)) a) (/ (neg (acos a)) a)) (/ (neg (acos a)) a))) (* (cbrt (/ 1 (/ (neg (acos a)) a))) (cbrt (/ 1 (/ (neg (acos a)) a)))) (cbrt (/ 1 (/ (neg (acos a)) a))) (* (* (/ 1 (/ (neg (acos a)) a)) (/ 1 (/ (neg (acos a)) a))) (/ 1 (/ (neg (acos a)) a))) (sqrt (/ 1 (/ (neg (acos a)) a))) (sqrt (/ 1 (/ (neg (acos a)) a))) (neg 1) (neg (/ (neg (acos a)) a)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (neg (acos a)) a)) (cbrt (/ (neg (acos a)) a)))) (/ (cbrt 1) (cbrt (/ (neg (acos a)) a))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (/ (neg (acos a)) a))) (/ (cbrt 1) (sqrt (/ (neg (acos a)) a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (neg (acos a))) (cbrt (neg (acos a)))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (cbrt (neg (acos a))) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (neg (acos a))) (cbrt (neg (acos a)))) (sqrt a))) (/ (cbrt 1) (/ (cbrt (neg (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (neg (acos a))) (cbrt (neg (acos a)))) 1)) (/ (cbrt 1) (/ (cbrt (neg (acos a))) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (neg (acos a))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (sqrt (neg (acos a))) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (neg (acos a))) (sqrt a))) (/ (cbrt 1) (/ (sqrt (neg (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (neg (acos a))) 1)) (/ (cbrt 1) (/ (sqrt (neg (acos a))) a)) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (neg (acos a)) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt a))) (/ (cbrt 1) (/ (neg (acos a)) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (cbrt 1) (/ (neg (acos a)) a)) (/ (* (cbrt 1) (cbrt 1)) (/ -1 (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (acos a) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ -1 (sqrt a))) (/ (cbrt 1) (/ (acos a) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ -1 1)) (/ (cbrt 1) (/ (acos a) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (neg (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (cbrt (acos a)) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (neg (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a))) (/ (cbrt 1) (/ (cbrt (acos a)) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (neg (* (cbrt (acos a)) (cbrt (acos a)))) 1)) (/ (cbrt 1) (/ (cbrt (acos a)) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (neg (sqrt (acos a))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (sqrt (acos a)) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (neg (sqrt (acos a))) (sqrt a))) (/ (cbrt 1) (/ (sqrt (acos a)) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (neg (sqrt (acos a))) 1)) (/ (cbrt 1) (/ (sqrt (acos a)) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (neg 1) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (acos a) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (neg 1) (sqrt a))) (/ (cbrt 1) (/ (acos a) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (neg 1) 1)) (/ (cbrt 1) (/ (acos a) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (neg (cbrt (acos a))) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (sqrt a))) (/ (cbrt 1) (/ (neg (cbrt (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) 1)) (/ (cbrt 1) (/ (neg (cbrt (acos a))) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (neg (sqrt (acos a))) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) (sqrt a))) (/ (cbrt 1) (/ (neg (sqrt (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) 1)) (/ (cbrt 1) (/ (neg (sqrt (acos a))) a)) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (neg (acos a)) (cbrt a))) (/ (* (cbrt 1) (cbrt 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-1 (/ 1 (acos a))) a (/ a (neg (acos a))) (/ (neg (acos a)) a) (/ (/ 1 (cbrt (/ (neg (acos a)) a))) (cbrt (/ (neg (acos a)) a))) (/ 1 (sqrt (/ (neg (acos a)) a))) (/ (* (cbrt a) (cbrt a)) (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ (sqrt a) (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ 1 (* (cbrt (neg (acos a))) (cbrt (neg (acos a))))) (/ (* (cbrt a) (cbrt a)) (sqrt (neg (acos a)))) (/ (sqrt a) (sqrt (neg (acos a)))) (/ 1 (sqrt (neg (acos a)))) (* (cbrt a) (cbrt a)) (sqrt a) 1 (* -1 (* (cbrt a) (cbrt a))) (* -1 (sqrt a)) -1 (/ (* (cbrt a) (cbrt a)) (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt a) (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (neg (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt a) (cbrt a)) (neg (sqrt (acos a)))) (/ (sqrt a) (neg (sqrt (acos a)))) (/ 1 (neg (sqrt (acos a)))) (* -1 (* (cbrt a) (cbrt a))) (* -1 (sqrt a)) -1 (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) (/ (sqrt a) (sqrt (acos a))) (/ 1 (sqrt (acos a))) (* (cbrt a) (cbrt a)) (sqrt a) 1 1 (* -1 (/ 1 (acos a))) (/ (neg (acos a)) a) (/ (neg (acos a)) a) (/ (neg (acos a)) a) (* -1 (/ 1 (acos a))) (log (/ (neg (acos a)) a)) (log (/ (neg (acos a)) a)) (exp (/ (neg (acos a)) a)) (pow (/ (neg (acos a)) a) 3) (* (cbrt (/ (neg (acos a)) a)) (cbrt (/ (neg (acos a)) a))) (cbrt (/ (neg (acos a)) a)) (pow (/ (neg (acos a)) a) 3) (sqrt (/ (neg (acos a)) a)) (sqrt (/ (neg (acos a)) a)) (acos a) (neg a) 0 (/ (acos a) a) (/ (* (cbrt (neg (acos a))) (cbrt (neg (acos a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (neg (acos a))) (cbrt a)) (/ (* (cbrt (neg (acos a))) (cbrt (neg (acos a)))) (sqrt a)) (/ (cbrt (neg (acos a))) (sqrt a)) (* (cbrt (neg (acos a))) (cbrt (neg (acos a)))) (/ (cbrt (neg (acos a))) a) (/ (sqrt (neg (acos a))) (* (cbrt a) (cbrt a))) (/ (sqrt (neg (acos a))) (cbrt a)) (/ (sqrt (neg (acos a))) (sqrt a)) (/ (sqrt (neg (acos a))) (sqrt a)) (sqrt (neg (acos a))) (/ (sqrt (neg (acos a))) a) (/ 1 (* (cbrt a) (cbrt a))) (/ (neg (acos a)) (cbrt a)) (/ 1 (sqrt a)) (/ (neg (acos a)) (sqrt a)) 1 (/ (neg (acos a)) a) (/ -1 (* (cbrt a) (cbrt a))) (/ (acos a) (cbrt a)) (/ -1 (sqrt a)) (/ (acos a) (sqrt a)) -1 (/ (acos a) a) (/ (neg (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (acos a)) (cbrt a)) (/ (neg (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)) (/ (cbrt (acos a)) (sqrt a)) (neg (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt (acos a)) a) (/ (neg (sqrt (acos a))) (* (cbrt a) (cbrt a))) (/ (sqrt (acos a)) (cbrt a)) (/ (neg (sqrt (acos a))) (sqrt a)) (/ (sqrt (acos a)) (sqrt a)) (neg (sqrt (acos a))) (/ (sqrt (acos a)) a) (/ -1 (* (cbrt a) (cbrt a))) (/ (acos a) (cbrt a)) (/ -1 (sqrt a)) (/ (acos a) (sqrt a)) -1 (/ (acos a) a) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))) (/ (neg (cbrt (acos a))) (cbrt a)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (sqrt a)) (/ (neg (cbrt (acos a))) (sqrt a)) (* (cbrt (acos a)) (cbrt (acos a))) (/ (neg (cbrt (acos a))) a) (/ (sqrt (acos a)) (* (cbrt a) (cbrt a))) (/ (neg (sqrt (acos a))) (cbrt a)) (/ (sqrt (acos a)) (sqrt a)) (/ (neg (sqrt (acos a))) (sqrt a)) (sqrt (acos a)) (/ (neg (sqrt (acos a))) a) (/ 1 (* (cbrt a) (cbrt a))) (/ (neg (acos a)) (cbrt a)) (/ 1 (sqrt a)) (/ (neg (acos a)) (sqrt a)) 1 (/ (neg (acos a)) a) (/ 1 a) (/ a (neg (acos a))) (/ (acos a) a) (/ (neg (acos a)) (* (cbrt a) (cbrt a))) (/ (neg (acos a)) (sqrt a)) (neg (acos a)) (/ a (cbrt (neg (acos a)))) (/ a (sqrt (neg (acos a)))) (/ a (neg (acos a))) (/ a (acos a)) (/ a (cbrt (acos a))) (/ a (sqrt (acos a))) (/ a (acos a)) (/ a (neg (cbrt (acos a)))) (/ a (neg (sqrt (acos a)))) (/ a (neg (acos a))) (/ a (neg (acos a))) (/ a (neg (acos a))) (/ a (neg (acos a))) (/ (neg (acos a)) a) (/ (neg (acos a)) a) (/ (neg (acos a)) a) 0.406 * * * [progress]: adding candidates to table 0.608 * * [progress]: iteration 3 / 4 0.608 * * * [progress]: picking best candidate 0.628 * * * * [pick]: Picked # 0.628 * * * [progress]: localizing error 0.634 * * * [progress]: generating rewritten candidates 0.634 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.643 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1 2) 0.650 * * * [progress]: generating series expansions 0.650 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.650 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.650 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.650 * [taylor]: Taking taylor expansion of -1 in a 0.651 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.651 * [taylor]: Taking taylor expansion of a in a 0.651 * [taylor]: Taking taylor expansion of (acos a) in a 0.651 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.651 * [taylor]: Taking taylor expansion of -1 in a 0.651 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.651 * [taylor]: Taking taylor expansion of a in a 0.651 * [taylor]: Taking taylor expansion of (acos a) in a 0.658 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.658 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.658 * [taylor]: Taking taylor expansion of -1 in a 0.658 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.658 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.658 * [taylor]: Taking taylor expansion of a in a 0.658 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.658 * [taylor]: Taking taylor expansion of -1 in a 0.658 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.658 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.658 * [taylor]: Taking taylor expansion of a in a 0.664 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.664 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.664 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.664 * [taylor]: Taking taylor expansion of a in a 0.664 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.665 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.665 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.665 * [taylor]: Taking taylor expansion of a in a 0.665 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.673 * * * * [progress]: [ 2 / 2 ] generating series at (2 1 2) 0.674 * [approximate]: Taking taylor expansion of (/ 1 (acos a)) in (a) around 0 0.674 * [taylor]: Taking taylor expansion of (/ 1 (acos a)) in a 0.674 * [taylor]: Taking taylor expansion of (acos a) in a 0.674 * [taylor]: Taking taylor expansion of (/ 1 (acos a)) in a 0.674 * [taylor]: Taking taylor expansion of (acos a) in a 0.675 * [approximate]: Taking taylor expansion of (/ 1 (acos (/ 1 a))) in (a) around 0 0.675 * [taylor]: Taking taylor expansion of (/ 1 (acos (/ 1 a))) in a 0.675 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.675 * [taylor]: Taking taylor expansion of (/ 1 (acos (/ 1 a))) in a 0.675 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.677 * [approximate]: Taking taylor expansion of (/ 1 (acos (/ -1 a))) in (a) around 0 0.677 * [taylor]: Taking taylor expansion of (/ 1 (acos (/ -1 a))) in a 0.677 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.677 * [taylor]: Taking taylor expansion of (/ 1 (acos (/ -1 a))) in a 0.677 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.678 * * * [progress]: simplifying candidates 0.680 * [simplify]: Simplifying using # : (- (+ (log -1) (neg (log (acos a)))) (neg (log a))) (- (+ (log -1) (neg (log (acos a)))) (- 0 (log a))) (- (+ (log -1) (neg (log (acos a)))) (- (log 1) (log a))) (- (+ (log -1) (neg (log (acos a)))) (log (/ 1 a))) (- (+ (log -1) (- 0 (log (acos a)))) (neg (log a))) (- (+ (log -1) (- 0 (log (acos a)))) (- 0 (log a))) (- (+ (log -1) (- 0 (log (acos a)))) (- (log 1) (log a))) (- (+ (log -1) (- 0 (log (acos a)))) (log (/ 1 a))) (- (+ (log -1) (- (log 1) (log (acos a)))) (neg (log a))) (- (+ (log -1) (- (log 1) (log (acos a)))) (- 0 (log a))) (- (+ (log -1) (- (log 1) (log (acos a)))) (- (log 1) (log a))) (- (+ (log -1) (- (log 1) (log (acos a)))) (log (/ 1 a))) (- (+ (log -1) (log (/ 1 (acos a)))) (neg (log a))) (- (+ (log -1) (log (/ 1 (acos a)))) (- 0 (log a))) (- (+ (log -1) (log (/ 1 (acos a)))) (- (log 1) (log a))) (- (+ (log -1) (log (/ 1 (acos a)))) (log (/ 1 a))) (- (log (* -1 (/ 1 (acos a)))) (neg (log a))) (- (log (* -1 (/ 1 (acos a)))) (- 0 (log a))) (- (log (* -1 (/ 1 (acos a)))) (- (log 1) (log a))) (- (log (* -1 (/ 1 (acos a)))) (log (/ 1 a))) (log (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (exp (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (/ (* (* (* -1 -1) -1) (/ (* (* 1 1) 1) (* (* (acos a) (acos a)) (acos a)))) (/ (* (* 1 1) 1) (* (* a a) a))) (/ (* (* (* -1 -1) -1) (/ (* (* 1 1) 1) (* (* (acos a) (acos a)) (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a))) (/ (* (* (* -1 -1) -1) (* (* (/ 1 (acos a)) (/ 1 (acos a))) (/ 1 (acos a)))) (/ (* (* 1 1) 1) (* (* a a) a))) (/ (* (* (* -1 -1) -1) (* (* (/ 1 (acos a)) (/ 1 (acos a))) (/ 1 (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a))) (/ (* (* (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a)))) (* -1 (/ 1 (acos a)))) (/ (* (* 1 1) 1) (* (* a a) a))) (/ (* (* (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a)))) (* -1 (/ 1 (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a))) (* (cbrt (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (cbrt (/ (* -1 (/ 1 (acos a))) (/ 1 a)))) (cbrt (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (* (* (/ (* -1 (/ 1 (acos a))) (/ 1 a)) (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (sqrt (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (sqrt (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (neg (* -1 (/ 1 (acos a)))) (neg (/ 1 a)) (/ -1 (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (/ (/ 1 (acos a)) (cbrt (/ 1 a))) (/ -1 (sqrt (/ 1 a))) (/ (/ 1 (acos a)) (sqrt (/ 1 a))) (/ -1 (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))) (/ (/ 1 (acos a)) (/ (cbrt 1) (cbrt a))) (/ -1 (/ (* (cbrt 1) (cbrt 1)) (sqrt a))) (/ (/ 1 (acos a)) (/ (cbrt 1) (sqrt a))) (/ -1 (/ (* (cbrt 1) (cbrt 1)) 1)) (/ (/ 1 (acos a)) (/ (cbrt 1) a)) (/ -1 (/ (sqrt 1) (* (cbrt a) (cbrt a)))) (/ (/ 1 (acos a)) (/ (sqrt 1) (cbrt a))) (/ -1 (/ (sqrt 1) (sqrt a))) (/ (/ 1 (acos a)) (/ (sqrt 1) (sqrt a))) (/ -1 (/ (sqrt 1) 1)) (/ (/ 1 (acos a)) (/ (sqrt 1) a)) (/ -1 (/ 1 (* (cbrt a) (cbrt a)))) (/ (/ 1 (acos a)) (/ 1 (cbrt a))) (/ -1 (/ 1 (sqrt a))) (/ (/ 1 (acos a)) (/ 1 (sqrt a))) (/ -1 (/ 1 1)) (/ (/ 1 (acos a)) (/ 1 a)) (/ -1 1) (/ (/ 1 (acos a)) (/ 1 a)) (/ -1 1) (/ (/ 1 (acos a)) (/ 1 a)) (/ 1 (/ 1 a)) (/ (/ 1 a) (* -1 (/ 1 (acos a)))) (/ (/ 1 (acos a)) (/ 1 a)) (/ (* -1 (/ 1 (acos a))) (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (/ (* -1 (/ 1 (acos a))) (sqrt (/ 1 a))) (/ (* -1 (/ 1 (acos a))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))) (/ (* -1 (/ 1 (acos a))) (/ (* (cbrt 1) (cbrt 1)) (sqrt a))) (/ (* -1 (/ 1 (acos a))) (/ (* (cbrt 1) (cbrt 1)) 1)) (/ (* -1 (/ 1 (acos a))) (/ (sqrt 1) (* (cbrt a) (cbrt a)))) (/ (* -1 (/ 1 (acos a))) (/ (sqrt 1) (sqrt a))) (/ (* -1 (/ 1 (acos a))) (/ (sqrt 1) 1)) (/ (* -1 (/ 1 (acos a))) (/ 1 (* (cbrt a) (cbrt a)))) (/ (* -1 (/ 1 (acos a))) (/ 1 (sqrt a))) (/ (* -1 (/ 1 (acos a))) (/ 1 1)) (/ (* -1 (/ 1 (acos a))) 1) (/ (* -1 (/ 1 (acos a))) 1) (/ (/ 1 a) (/ 1 (acos a))) (/ (* -1 (/ 1 (acos a))) 1) (* (/ 1 a) (acos a)) (* (/ 1 a) (acos a)) (neg 1) (neg (log (acos a))) (- 0 (log (acos a))) (- (log 1) (log (acos a))) (log (/ 1 (acos a))) (exp (/ 1 (acos a))) (/ (* (* 1 1) 1) (* (* (acos a) (acos a)) (acos a))) (* (cbrt (/ 1 (acos a))) (cbrt (/ 1 (acos a)))) (cbrt (/ 1 (acos a))) (* (* (/ 1 (acos a)) (/ 1 (acos a))) (/ 1 (acos a))) (sqrt (/ 1 (acos a))) (sqrt (/ 1 (acos a))) (neg 1) (neg (acos a)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt 1) (cbrt (acos a))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (acos a))) (/ (cbrt 1) (sqrt (acos a))) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (acos a)) (/ (sqrt 1) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt 1) (cbrt (acos a))) (/ (sqrt 1) (sqrt (acos a))) (/ (sqrt 1) (sqrt (acos a))) (/ (sqrt 1) 1) (/ (sqrt 1) (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (cbrt (acos a))) (/ 1 (sqrt (acos a))) (/ 1 (sqrt (acos a))) (/ 1 1) (/ 1 (acos a)) (/ 1 (acos a)) (/ (acos a) 1) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ 1 1) (/ (acos a) (cbrt 1)) (/ (acos a) (sqrt 1)) (/ (acos a) 1) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (/ 1 (acos a)) (/ 1 (acos a)) (/ 1 (acos a)) 0.685 * * [simplify]: iteration 0 : 475 enodes (cost 613 ) 0.695 * * [simplify]: iteration 1 : 2489 enodes (cost 473 ) 0.729 * * [simplify]: iteration 2 : 5001 enodes (cost 428 ) 0.732 * [simplify]: Simplified to: (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (+ (log (/ -1 (acos a))) (log a)) (pow (exp (/ -1 (acos a))) a) (pow (* (/ -1 (acos a)) a) 3) (pow (* (/ -1 (acos a)) a) 3) (pow (* (/ -1 (acos a)) a) 3) (pow (* (/ -1 (acos a)) a) 3) (pow (* (/ -1 (acos a)) a) 3) (pow (* (/ -1 (acos a)) a) 3) (* (cbrt (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (cbrt (/ (* -1 (/ 1 (acos a))) (/ 1 a)))) (cbrt (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (pow (* (/ -1 (acos a)) a) 3) (sqrt (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (sqrt (/ (* -1 (/ 1 (acos a))) (/ 1 a))) (/ 1 (acos a)) (/ -1 a) (/ -1 (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (/ (/ 1 (acos a)) (cbrt (/ 1 a))) (/ -1 (sqrt (/ 1 a))) (/ (/ 1 (acos a)) (sqrt (/ 1 a))) (* -1 (* (cbrt a) (cbrt a))) (* (/ 1 (acos a)) (cbrt a)) (* -1 (sqrt a)) (* (/ 1 (acos a)) (sqrt a)) -1 (/ a (acos a)) (* -1 (* (cbrt a) (cbrt a))) (* (/ 1 (acos a)) (cbrt a)) (* -1 (sqrt a)) (* (/ 1 (acos a)) (sqrt a)) -1 (/ a (acos a)) (* -1 (* (cbrt a) (cbrt a))) (* (/ 1 (acos a)) (cbrt a)) (* -1 (sqrt a)) (* (/ 1 (acos a)) (sqrt a)) -1 (/ a (acos a)) -1 (/ a (acos a)) -1 (/ a (acos a)) a (* -1 (/ (acos a) a)) (/ a (acos a)) (/ (/ (/ -1 (acos a)) (cbrt (/ 1 a))) (cbrt (/ 1 a))) (/ -1 (* (sqrt (/ 1 a)) (acos a))) (* (/ -1 (acos a)) (* (cbrt a) (cbrt a))) (* (/ -1 (acos a)) (sqrt a)) (/ -1 (acos a)) (* (/ -1 (acos a)) (* (cbrt a) (cbrt a))) (* (/ -1 (acos a)) (sqrt a)) (/ -1 (acos a)) (* (/ -1 (acos a)) (* (cbrt a) (cbrt a))) (* (/ -1 (acos a)) (sqrt a)) (/ -1 (acos a)) (/ -1 (acos a)) (/ -1 (acos a)) (/ (acos a) a) (/ -1 (acos a)) (/ (acos a) a) (/ (acos a) a) -1 (log (/ 1 (acos a))) (log (/ 1 (acos a))) (log (/ 1 (acos a))) (log (/ 1 (acos a))) (exp (/ 1 (acos a))) (/ 1 (pow (acos a) 3)) (* (cbrt (/ 1 (acos a))) (cbrt (/ 1 (acos a)))) (cbrt (/ 1 (acos a))) (/ 1 (pow (acos a) 3)) (sqrt (/ 1 (acos a))) (sqrt (/ 1 (acos a))) -1 (neg (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (cbrt (acos a))) (/ 1 (sqrt (acos a))) (/ 1 (sqrt (acos a))) 1 (/ 1 (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (cbrt (acos a))) (/ 1 (sqrt (acos a))) (/ 1 (sqrt (acos a))) 1 (/ 1 (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (cbrt (acos a))) (/ 1 (sqrt (acos a))) (/ 1 (sqrt (acos a))) 1 (/ 1 (acos a)) (/ 1 (acos a)) (acos a) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (sqrt (acos a))) 1 (acos a) (acos a) (acos a) (* (/ -1 (acos a)) a) (* (/ -1 (acos a)) a) (* (/ -1 (acos a)) a) (/ 1 (acos a)) (/ 1 (acos a)) (/ 1 (acos a)) 0.733 * * * [progress]: adding candidates to table 0.821 * * [progress]: iteration 4 / 4 0.821 * * * [progress]: picking best candidate 0.829 * * * * [pick]: Picked # 0.829 * * * [progress]: localizing error 0.835 * * * [progress]: generating rewritten candidates 0.835 * * * * [progress]: [ 1 / 2 ] rewriting at (2 2) 0.844 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 0.854 * * * [progress]: generating series expansions 0.854 * * * * [progress]: [ 1 / 2 ] generating series at (2 2) 0.854 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.854 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.854 * [taylor]: Taking taylor expansion of -1 in a 0.854 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.854 * [taylor]: Taking taylor expansion of (acos a) in a 0.854 * [taylor]: Taking taylor expansion of a in a 0.854 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.854 * [taylor]: Taking taylor expansion of -1 in a 0.854 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.854 * [taylor]: Taking taylor expansion of (acos a) in a 0.854 * [taylor]: Taking taylor expansion of a in a 0.868 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.868 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.868 * [taylor]: Taking taylor expansion of -1 in a 0.868 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.868 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.868 * [taylor]: Taking taylor expansion of a in a 0.868 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.868 * [taylor]: Taking taylor expansion of -1 in a 0.868 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.868 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.868 * [taylor]: Taking taylor expansion of a in a 0.879 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.879 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.879 * [taylor]: Taking taylor expansion of a in a 0.879 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.879 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.879 * [taylor]: Taking taylor expansion of a in a 0.879 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.891 * * * * [progress]: [ 2 / 2 ] generating series at (2) 0.891 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.891 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.891 * [taylor]: Taking taylor expansion of -1 in a 0.891 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.891 * [taylor]: Taking taylor expansion of a in a 0.891 * [taylor]: Taking taylor expansion of (acos a) in a 0.891 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.891 * [taylor]: Taking taylor expansion of -1 in a 0.891 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.891 * [taylor]: Taking taylor expansion of a in a 0.891 * [taylor]: Taking taylor expansion of (acos a) in a 0.898 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.898 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.898 * [taylor]: Taking taylor expansion of -1 in a 0.898 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.898 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.898 * [taylor]: Taking taylor expansion of a in a 0.898 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.898 * [taylor]: Taking taylor expansion of -1 in a 0.898 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.898 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.898 * [taylor]: Taking taylor expansion of a in a 0.904 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.904 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.904 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.904 * [taylor]: Taking taylor expansion of a in a 0.904 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.905 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.905 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.905 * [taylor]: Taking taylor expansion of a in a 0.905 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.913 * * * [progress]: simplifying candidates 0.915 * [simplify]: Simplifying using # : (* (neg (acos a)) (/ 1 a)) (+ (log (neg (acos a))) (neg (log a))) (+ (log (neg (acos a))) (- 0 (log a))) (+ (log (neg (acos a))) (- (log 1) (log a))) (+ (log (neg (acos a))) (log (/ 1 a))) (log (* (neg (acos a)) (/ 1 a))) (exp (* (neg (acos a)) (/ 1 a))) (* (* (* (neg (acos a)) (neg (acos a))) (neg (acos a))) (/ (* (* 1 1) 1) (* (* a a) a))) (* (* (* (neg (acos a)) (neg (acos a))) (neg (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a))) (* (cbrt (* (neg (acos a)) (/ 1 a))) (cbrt (* (neg (acos a)) (/ 1 a)))) (cbrt (* (neg (acos a)) (/ 1 a))) (* (* (* (neg (acos a)) (/ 1 a)) (* (neg (acos a)) (/ 1 a))) (* (neg (acos a)) (/ 1 a))) (sqrt (* (neg (acos a)) (/ 1 a))) (sqrt (* (neg (acos a)) (/ 1 a))) (* (sqrt (neg (acos a))) (sqrt (/ 1 a))) (* (sqrt (neg (acos a))) (sqrt (/ 1 a))) (* (sqrt (neg (acos a))) (/ (sqrt 1) (sqrt a))) (* (sqrt (neg (acos a))) (/ (sqrt 1) (sqrt a))) (* (sqrt (neg (acos a))) (/ 1 (sqrt a))) (* (sqrt (neg (acos a))) (/ 1 (sqrt a))) (* (acos a) (/ 1 a)) (* (neg (acos a)) (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (neg (acos a)) (sqrt (/ 1 a))) (* (neg (acos a)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))) (* (neg (acos a)) (/ (* (cbrt 1) (cbrt 1)) (sqrt a))) (* (neg (acos a)) (/ (* (cbrt 1) (cbrt 1)) 1)) (* (neg (acos a)) (/ (sqrt 1) (* (cbrt a) (cbrt a)))) (* (neg (acos a)) (/ (sqrt 1) (sqrt a))) (* (neg (acos a)) (/ (sqrt 1) 1)) (* (neg (acos a)) (/ 1 (* (cbrt a) (cbrt a)))) (* (neg (acos a)) (/ 1 (sqrt a))) (* (neg (acos a)) (/ 1 1)) (* (neg (acos a)) 1) (* (neg (acos a)) 1) (* (cbrt (neg (acos a))) (/ 1 a)) (* (sqrt (neg (acos a))) (/ 1 a)) (* (neg (acos a)) (/ 1 a)) (* (acos a) (/ 1 a)) (* (cbrt (acos a)) (/ 1 a)) (* (sqrt (acos a)) (/ 1 a)) (* (acos a) (/ 1 a)) (* (neg (cbrt (acos a))) (/ 1 a)) (* (neg (sqrt (acos a))) (/ 1 a)) (* (neg (acos a)) (/ 1 a)) (* (neg (acos a)) 1) (neg 1) (neg 1) (neg (+ (log (neg (acos a))) (neg (log a)))) (neg (+ (log (neg (acos a))) (- 0 (log a)))) (neg (+ (log (neg (acos a))) (- (log 1) (log a)))) (neg (+ (log (neg (acos a))) (log (/ 1 a)))) (neg (log (* (neg (acos a)) (/ 1 a)))) (- 0 (+ (log (neg (acos a))) (neg (log a)))) (- 0 (+ (log (neg (acos a))) (- 0 (log a)))) (- 0 (+ (log (neg (acos a))) (- (log 1) (log a)))) (- 0 (+ (log (neg (acos a))) (log (/ 1 a)))) (- 0 (log (* (neg (acos a)) (/ 1 a)))) (- (log 1) (+ (log (neg (acos a))) (neg (log a)))) (- (log 1) (+ (log (neg (acos a))) (- 0 (log a)))) (- (log 1) (+ (log (neg (acos a))) (- (log 1) (log a)))) (- (log 1) (+ (log (neg (acos a))) (log (/ 1 a)))) (- (log 1) (log (* (neg (acos a)) (/ 1 a)))) (log (/ 1 (* (neg (acos a)) (/ 1 a)))) (exp (/ 1 (* (neg (acos a)) (/ 1 a)))) (/ (* (* 1 1) 1) (* (* (* (neg (acos a)) (neg (acos a))) (neg (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))) (/ (* (* 1 1) 1) (* (* (* (neg (acos a)) (neg (acos a))) (neg (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))) (/ (* (* 1 1) 1) (* (* (* (neg (acos a)) (/ 1 a)) (* (neg (acos a)) (/ 1 a))) (* (neg (acos a)) (/ 1 a)))) (* (cbrt (/ 1 (* (neg (acos a)) (/ 1 a)))) (cbrt (/ 1 (* (neg (acos a)) (/ 1 a))))) (cbrt (/ 1 (* (neg (acos a)) (/ 1 a)))) (* (* (/ 1 (* (neg (acos a)) (/ 1 a))) (/ 1 (* (neg (acos a)) (/ 1 a)))) (/ 1 (* (neg (acos a)) (/ 1 a)))) (sqrt (/ 1 (* (neg (acos a)) (/ 1 a)))) (sqrt (/ 1 (* (neg (acos a)) (/ 1 a)))) (neg 1) (neg (* (neg (acos a)) (/ 1 a))) (/ (* (cbrt 1) (cbrt 1)) (neg (acos a))) (/ (cbrt 1) (/ 1 a)) (/ (sqrt 1) (neg (acos a))) (/ (sqrt 1) (/ 1 a)) (/ 1 (neg (acos a))) (/ 1 (/ 1 a)) (/ 1 (* (neg (acos a)) (/ 1 a))) (/ (* (neg (acos a)) (/ 1 a)) 1) (/ 1 (neg (acos a))) (/ (* (neg (acos a)) (/ 1 a)) (cbrt 1)) (/ (* (neg (acos a)) (/ 1 a)) (sqrt 1)) (/ (* (neg (acos a)) (/ 1 a)) 1) (/ 1 (neg (acos a))) (/ 1 (* (neg (acos a)) 1)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 0.920 * * [simplify]: iteration 0 : 351 enodes (cost 504 ) 0.927 * * [simplify]: iteration 1 : 1643 enodes (cost 400 ) 0.951 * * [simplify]: iteration 2 : 5001 enodes (cost 379 ) 0.953 * [simplify]: Simplified to: (/ (neg (acos a)) a) (log (/ (neg (acos a)) a)) (log (/ (neg (acos a)) a)) (log (/ (neg (acos a)) a)) (log (/ (neg (acos a)) a)) (log (/ (neg (acos a)) a)) (exp (/ (neg (acos a)) a)) (pow (/ (neg (acos a)) a) 3) (pow (/ (neg (acos a)) a) 3) (* (cbrt (* (neg (acos a)) (/ 1 a))) (cbrt (* (neg (acos a)) (/ 1 a)))) (cbrt (* (neg (acos a)) (/ 1 a))) (pow (/ (neg (acos a)) a) 3) (sqrt (* (neg (acos a)) (/ 1 a))) (sqrt (* (neg (acos a)) (/ 1 a))) (* (sqrt (neg (acos a))) (sqrt (/ 1 a))) (* (sqrt (neg (acos a))) (sqrt (/ 1 a))) (/ (* (sqrt (neg (acos a))) 1) (sqrt a)) (/ (* (sqrt (neg (acos a))) 1) (sqrt a)) (/ (* (sqrt (neg (acos a))) 1) (sqrt a)) (/ (* (sqrt (neg (acos a))) 1) (sqrt a)) (/ (acos a) a) (* (neg (acos a)) (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (neg (acos a)) (sqrt (/ 1 a))) (/ (* (acos a) -1) (* (cbrt a) (cbrt a))) (/ (* (acos a) -1) (sqrt a)) (* (acos a) -1) (/ (* (acos a) -1) (* (cbrt a) (cbrt a))) (/ (* (acos a) -1) (sqrt a)) (* (acos a) -1) (/ (* (acos a) -1) (* (cbrt a) (cbrt a))) (/ (* (acos a) -1) (sqrt a)) (* (acos a) -1) (* (acos a) -1) (* (acos a) -1) (/ (cbrt (neg (acos a))) a) (/ (sqrt (neg (acos a))) a) (/ (neg (acos a)) a) (/ (acos a) a) (/ (cbrt (acos a)) a) (/ (sqrt (acos a)) a) (/ (acos a) a) (/ (neg (cbrt (acos a))) a) (/ (neg (sqrt (acos a))) a) (/ (neg (acos a)) a) (* (acos a) -1) -1 -1 (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (neg (log (/ (neg (acos a)) a))) (pow (exp (/ 1 (neg (acos a)))) a) (/ (pow a 3) (pow (neg (acos a)) 3)) (/ (pow a 3) (pow (neg (acos a)) 3)) (/ (pow a 3) (pow (neg (acos a)) 3)) (* (cbrt (/ 1 (* (neg (acos a)) (/ 1 a)))) (cbrt (/ 1 (* (neg (acos a)) (/ 1 a))))) (cbrt (/ 1 (* (neg (acos a)) (/ 1 a)))) (/ (pow a 3) (pow (neg (acos a)) 3)) (sqrt (/ 1 (* (neg (acos a)) (/ 1 a)))) (sqrt (/ 1 (* (neg (acos a)) (/ 1 a)))) -1 (/ (acos a) a) (* (/ 1 (acos a)) -1) a (* (/ 1 (acos a)) -1) a (* (/ 1 (acos a)) -1) a (/ a (neg (acos a))) (/ (neg (acos a)) a) (* (/ 1 (acos a)) -1) (/ (neg (acos a)) a) (/ (neg (acos a)) a) (/ (neg (acos a)) a) (* (/ 1 (acos a)) -1) (* (/ 1 (acos a)) -1) (/ (neg (acos a)) a) (/ (neg (acos a)) a) (/ (neg (acos a)) a) (/ a (neg (acos a))) (/ a (neg (acos a))) (/ a (neg (acos a))) 0.954 * * * [progress]: adding candidates to table 1.039 * [progress]: [Phase 3 of 3] Extracting. 1.039 * * [regime]: Finding splitpoints for: (# # # # # # #) 1.040 * * * [regime-changes]: Trying 2 branch expressions: ((/ a (neg (acos a))) a) 1.040 * * * * [regimes]: Trying to branch on (/ a (neg (acos a))) from (# # # # # # #) 1.067 * * * * [regimes]: Trying to branch on a from (# # # # # # #) 1.087 * * * [regime]: Found split indices: #